Question

11) Consider an electromagnetic type radiation that is contained within a cavity and is in equilibrium with the walls of that cavity (cavity radiation) that can be seen as a hydrostatic system, whose internal energy density and the pressure p exerted under the cavity walls are given by 1 U V u(T) P= where V is the volume of the cavity and T is the temperature of the cavity walls. Considering the energy density u = aT', where a is a constant. a) Consider an isothermal and reversible compression of the volume of the V1 cavity to the V2 volume and determine the work W performed under the radiation, the heat Q eliminated by the radiation and the entropy variation AS of the radiation. Represent the process on a p - V diagram.

Answer 1

UIT) U(T) = -4 Process Given - Internal energy density u. Yu aT Pressure P= I u For iso thermal Volume and Volume ķ performed under Heat eleminated O and in entropy _DS Thermodynamich where 8 Erity 1-Y of Cavity Work done Radiation charge Now using First low W d OU 2 4 DO ou= o- su=aut di U(T) = AT" (Diven) 8 Work done W = d - 4a T3 dt / I Work done in P-V Work done for Isothermal Process can also find of digram :- I pp 1 . WznRT V li mole (P2 V ₂) R = Constant of god Ta constant Temp- V vw Shaded Area is work done. n=no. g P W u